On the mechanism of formation of diffusional plate-shaped transformation products
Introduction
Diffusional plate-like phase transformations, encompassing both high-temperature transformations and bainitic transformations [1], can proceed by the motion of transformation disconnections (defects with ledge/dislocation character [2]), by the motion of growth ledges (defects with pure ledge character or with negligible dislocation content [3]), or by a mixture of these. Mechanistic theories exist for transformation by both types of defect [4], [5]. Also, experiments reveal both types of defect in the interfaces of transformed alloys [6], [7] and show surface relief effects with surface displacements ranging from zero relief to large reliefs [8], [9]. The aim of the present study is to indicate that such a spectrum of behavior is consistent with a unified mechanistic model.
There have been many observations of surface tent-shaped and invariant-plane-strain surface reliefs, beginning with early work on ferrite by Ko [10], on θ allotriomorphs in Al–Cu [11], on Ag–Al [12], and on low-alloy steel [13], [14]. More recent studies have shown tent-shaped reliefs in a Ti–Cr alloy [15] and a Ti–Mo alloy [8]. A number of these observations are reviewed in Refs. [8], [9]. Several authors [16], [17], [18] suggested that the relief could be associated with the motion of defects with both ledge (or step) and dislocation character. If these defects have unit atomic height they correspond to the structural ledges of Hall et al. [19]. Hirth and Pond [20] have formally characterized these defects in terms of vector fields and circuits as disconnections, with dislocation content characterized by a Burgers vector and a step height characterized by the dichromatic pattern of the overlapping lattices. This description has been incorporated in phase transformation terminology [5] to describe moving defects as transformation disconnections (TDs), those spaced to remove long-range strains in an equilibrium interface as structural disconnections (SDs), and those present only to remove coherency strains as misfit disconnections (MDs). For certain specific ledge heights, the disconnections also correspond closely to Moiré ledges [21], [22] or to near O-lattice ledges [4].
There are also many observations of growth ledges (GLs), ranging up to micrometers in height [13], [4], [23]. These may have a small Burgers vector content, but it is essentially negligible compared to the ledge height h, so that they can be considered to be pure ledges. The GLs can be described by other models [20], [22], [4] but have a growth mechanism different from TDs, so we treat them as distinctive defects. In particular, the motion of GLs would produce no surface relief.
We now consider specific mechanisms for these different cases. We consider first the motion of defects on the broad faces of a growing plate where the line directions of the TDs and GLs are normal to the transformation direction (Fig. 1). The defects traverse low-index terraces, where the two phases are strained to be coherent. Also the Burgers vectors of the dislocation components, whose motion produces the glide displacement leading to surface relief, are considered to be pure edge in order to optimize coherency strain relief just as for SDs. The actual motion of a TD probably occurs by kink pair formation and motion as observed by Howe and Prabhu [24]. However, analogous to the case of ledge growth from the vapor [25], the kink spacing is likely to be such that the moving TDs act as local equilibrium line sources for diffusion and the lines remain nominally straight, so this interesting detail of the mechanism is neglected here. We also focus only on defect motion, neglecting the analysis of the necessary nucleation mechanism for the defects.
Section snippets
Motion of TDs
MonoTDs, those of unit height ha in the dichromatic pattern, have been observed using hot-stage transmission electron microscopy (TEM) to move in Al–Ag alloys [24], [26], [27]. There are few other observations of such motion for diffusional transformations. In the case of martensitic transformations, there are more observations of the motion of TDs, with observations of monoTDs [28] and biTDs [29]. When observed after transformation, there are a number of other observations of monoSDs, a recent
Formation and motion of GLs
Observations of GLs and models for their role in growth are discussed by Aaronson [37], [38]. There are several mechanisms of formation and motion of GLs. The first is the direct conversion of a superTD (Fig. 3): an equivalent to this process would be the absorption of an extrinsic dislocation from the matrix. Studies on Ti–Cr [39] and Ni–Cr [23], [40] have shown that a superTD converts to a GL by the formation of extrinsic perfect dislocations in the ledge riser with the emission of
Intermediate cases
There are also cases intermediate between pure TD motion and pure GL motion. These are of two types. First, Bo and Fang [14] suggest that the surface relief is narrower than the thickness of ferrite allotriomorphs. This would be consistent with a situation where the initial mechanism was one of TD motion. However, later, as the diffusion gradients decreased and, concomitantly, the driving force decreased, the TDs would become pinned and there would be a transition to growth by GL motion. In
Other considerations
In the preceding discussion, the TDs/SDs are usually assumed to have Burgers vectors in the edge orientation in order to maximize coherency strain relief. Other solutions for the habit plane are of course possible, consistent with theories for the crystallography of the transformation [20], [33]. These include the possibility of TDs/SDs in other than edge orientation. In such a case the accommodating dislocations may also be in other than edge orientation and several accommodation systems
Summary
Rather than being competing models, transformations by means of TDs and by means of GLs are part of a spectrum of possible transformation mechanisms in the formation of diffusional plate-shaped products. Evidence from measured relief angles and from theory supports one limiting case of transformation purely by TDs, of various possible heights. Other evidence from the absence of relief and observations in transformed structures supports the other limiting case of growth purely by GLs.
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